The Conservative Party chairman has told Sky News that Culture Secretary Maria Miller should be "allowed to get on with her job", despite calls for her to resign.

A new poll suggests most voters think she should be sacked over the way she dealt with an investigation into her expenses.

But asked if she had his 100% support, Grant Shapps told the Murnaghan show: "Yes, she does. Maria Miller is a very, very hard-working minister.

Image:Mrs Miller making her apology in Parliament on Thursday

"She has accepted fully the recommendations of the committee without reservation, and she should be able to get on with her job, and the Prime Minister has said that's what he wants her to do."

Pressed on whether she had his personal support, Mr Shapps replied: "Well, listen, I don't put her in the post ... She is somebody who, let's face it, has worked on a lot of tricky sensitive issues ... Leveson being one of them. So she has a portfolio which has happened to have been particularly complicated.

Video:Maria Miller 'Wouldn't Be Missed'

"Yes, she has gone through a complete process. She has done exactly what the committee asked her to do... And the Prime Minister has been clear that he is then satisfied with that and so, of course, I am satisfied with it as well."

Prime Minister David Cameron has been criticised for standing by Mrs Miller and is under pressure from Labour to show leadership.

But the Survation poll for the Mail on Sunday found 75% of the public think Mr Cameron was wrong to support her, compared with 14% who backed his decision to stand by her.

Some 78% of those surveyed said Mrs Miller should forfeit her Cabinet post as Culture Secretary.

Video:PM Moves On From Miller Money Row

And 66% said she should lose powers over press regulation while 68% said she should be "sacked" as an MP - something which is not currently possible, as the Government is yet to introduce the power of recall promised in the 2010 Coalition Agreement.

The Culture Secretary has paid back £5,800 of expenses she had wrongly claimed for a second home and made the brief apology in Parliament for her "unhelpful" attitude towards the investigation.

But she remains under pressure after it emerged the 10-member standards committee overruled the Parliamentary Commissioner for Standards' findings that she should return £45,000.

David Mellor, who resigned from John Major's Cabinet amid a scandal in 1992, told the Murnaghan show: "I don't think it matters whether she resigns or not.

Video:Maria Miller paper row escalates

"She won't be missed if she goes and she won't be noticed if she stays.

"What this is all about is first of all the judgement of David Cameron, and secondly the integrity of the British Parliament."

Meanwhile, there was further embarrassment for Mrs Miller when a string of mocking messages was sent out on the Twitter feed of her own Department for Culture, Media and Sport on Saturday evening.

The first bogus tweet from the @DCMS account said: "Seriously though guys which one of us hasn't embezzled and cheated the taxpayer?? #FreeMariaMiller"

The next one, posted a minute later, said: "@Maria--MillerMP is like a modern day Robin Hood, she robs the poor to help the rich".

And the third tweet said: "Is Maria @Maria--MillerMP guilty? We will let the public decide".

A spokeswoman from the DCMS said the department had "absolutely no idea" who was responsible.